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Exponential bounds for noncommuting systems of matrices

Brian Jefferies (2001)

Studia Mathematica

It is shown that a finite system T of matrices whose real linear combinations have real spectrum satisfies a bound of the form | | e i T , ζ | | C ( 1 + | ζ | ) s e r | ζ | . The proof appeals to the monogenic functional calculus.

Exponential-type Nagumo norms and summability of formal solutions of singular partial differential equations

Zhuangchu Luo, Hua Chen, Changgui Zhang (2012)

Annales de l’institut Fourier

In this paper, we study a class of first order nonlinear degenerate partial differential equations with singularity at ( t , x ) = ( 0 , 0 ) C 2 . Using exponential-type Nagumo norm approach, the Gevrey asymptotic analysis is extended to case of holomorphic parameters in a natural way. A sharp condition is then established to deduce the k -summability of the formal solutions. Furthermore, analytical solutions in conical domains are found for each type of these nonlinear singular PDEs.

Exposed points in the set of representing measures for the disc algebra

Alexander J. Izzo (1995)

Annales Polonici Mathematici

It is shown that for each nonzero point x in the open unit disc D, there is a measure whose support is exactly ∂D ∪ {x} and that is also a weak*-exposed point in the set of representing measures for the origin on the disc algebra. This yields a negative answer to a question raised by John Ryff.

Extending analyticK-subanalytic functions

Artur Piękosz (2004)

Open Mathematics

Letg:U→ℝ (U open in ℝn) be an analytic and K-subanalytic (i. e. definable in ℝanK, whereK, the field of exponents, is any subfield ofℝ) function. Then the set of points, denoted Σ, whereg does not admit an analytic extension is K-subanalytic andg can be extended analytically to a neighbourhood of Ū.

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